# Showing papers in "Physical Review B in 2006"

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TL;DR: In this paper, the authors derived closed expressions for the head of the frequency-dependent microscopic polarizability matrix in the projector-augmented wave (PAW) methodology, resulting in dielectric properties that are largely independent of the applied potentials.

Abstract: In this work we derive closed expressions for the head of the frequency-dependent microscopic polarizability matrix in the projector-augmented wave (PAW) methodology. Contrary to previous applications, the longitudinal expression is utilized, resulting in dielectric properties that are largely independent of the applied potentials. The improved accuracy of the present approach is demonstrated by comparing the longitudinal and transversal expressions of the polarizability matrix for a number of cubic semiconductors and one insulator, i.e., Si, SiC, AlP, GaAs, and diamond (C), respectively. The methodology is readily extendable to more complicated nonlocal Hamiltonians or to the calculation of the macroscopic dielectric matrix including local field effects in the random phase or density functional approximation, which is demonstrated for the previously mentioned model systems. Furthermore, density functional perturbation theory is extended to the PAW method, and the respective results are compared to those obtained by summation over the conduction band states.

2,394 citations

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TL;DR: In this paper, the energy of a large number of oxidation reactions of $3d$ transition metal oxides is computed using the generalized gradient approach (GGA) and γ-U + γ U methods.

Abstract: The energy of a large number of oxidation reactions of $3d$ transition metal oxides is computed using the generalized gradient approach (GGA) and $\mathrm{GGA}+\mathrm{U}$ methods Two substantial contributions to the error in GGA oxidation energies are identified The first contribution originates from the overbinding of GGA in the ${\mathrm{O}}_{2}$ molecule and only occurs when the oxidant is ${\mathrm{O}}_{2}$ The second error occurs in all oxidation reactions and is related to the correlation error in $3d$ orbitals in GGA Strong self-interaction in GGA systematically penalizes a reduced state (with more $d$ electrons) over an oxidized state, resulting in an overestimation of oxidation energies The constant error in the oxidation energy from the ${\mathrm{O}}_{2}$ binding error can be corrected by fitting the formation enthalpy of simple nontransition metal oxides Removal of the ${\mathrm{O}}_{2}$ binding error makes it possible to address the correlation effects in $3d$ transition metal oxides with the $\mathrm{GGA}+\mathrm{U}$ method Calculated oxidation energies agree well with experimental data for reasonable and consistent values of U

2,013 citations

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TL;DR: In this article, a non-empirical density functional generalized gradient approximation (GGA) was proposed for lattice constants, crystal structures, and metal surface energies, which is based on a diffuse radial cutoff for the exchange hole in real space, and the analytic gradient expansion of the exchange energy for small gradients.

Abstract: We present a nonempirical density functional generalized gradient approximation (GGA) that gives significant improvements for lattice constants, crystal structures, and metal surface energies over the most popular Perdew-Burke-Ernzerhof (PBE) GGA. The functional is based on a diffuse radial cutoff for the exchange hole in real space, and the analytic gradient expansion of the exchange energy for small gradients. There are no adjustable parameters, the constraining conditions of PBE are maintained, and the functional is easily implemented in existing codes.

1,783 citations

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TL;DR: In this paper, the electronic states of narrow graphene ribbons with zigzag and armchair edges were analyzed using the Dirac equation with appropriate boundary conditions, showing that the boundary condition allows a particlelike and a hole-like band with evanescent wave functions confined to the surfaces, which continuously turn into zero energy surface states as the width gets large.

Abstract: We study the electronic states of narrow graphene ribbons (``nanoribbons'') with zigzag and armchair edges. The finite width of these systems breaks the spectrum into an infinite set of bands, which we demonstrate can be quantitatively understood using the Dirac equation with appropriate boundary conditions. For the zigzag nanoribbon we demonstrate that the boundary condition allows a particlelike and a holelike band with evanescent wave functions confined to the surfaces, which continuously turn into the well-known zero energy surface states as the width gets large. For armchair edges, we show that the boundary condition leads to admixing of valley states, and the band structure is metallic when the width of the sample in lattice constant units has the form $3M+1$, with $M$ an integer, and insulating otherwise. A comparison of the wave functions and energies from tight-binding calculations and solutions of the Dirac equations yields quantitative agreement for all but the narrowest ribbons.

1,244 citations

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TL;DR: In this paper, it was shown that room-temperature ferromagnetism has been observed in nanoparticles of nonmagnetic oxides such as (1), (2), (3), (4), (5), (6), (7,30), and (6,30).

Abstract: Room-temperature ferromagnetism has been observed in nanoparticles $(7--30\phantom{\rule{0.3em}{0ex}}\mathrm{nm}\phantom{\rule{0.2em}{0ex}}\mathrm{diam})$ of nonmagnetic oxides such as ${\mathrm{CeO}}_{2}$, ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$, $\mathrm{ZnO}$, ${\mathrm{In}}_{2}{\mathrm{O}}_{3}$, and ${\mathrm{SnO}}_{2}$. The saturated magnetic moments in ${\mathrm{CeO}}_{2}$ and ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ nanoparticles are comparable to those observed in transition-metal-doped wideband semiconducting oxides. The other oxide nanoparticles show somewhat lower values of magnetization but with a clear hysteretic behavior. Conversely, the bulk samples obtained by sintering the nanoparticles at high temperatures in air or oxygen became diamagnetic. As there were no magnetic impurities present, we assume that the origin of ferromagnetism may be the exchange interactions between localized electron spin moments resulting from oxygen vacancies at the surfaces of nanoparticles. We suggest that ferromagnetism may be a universal characteristic of nanoparticles of metal oxides.

1,239 citations

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TL;DR: In this article, the effects of localized (impurities or vacancies) and extended (edges or grain boundaries) defects on the electronic and transport properties of graphene are analyzed in a self-consistent way.

Abstract: Two-dimensional carbon, or graphene, is a semimetal that presents unusual low-energy electronic excitations described in terms of Dirac fermions. We analyze in a self-consistent way the effects of localized (impurities or vacancies) and extended (edges or grain boundaries) defects on the electronic and transport properties of graphene. On the one hand, point defects induce a finite elastic lifetime at low energies with the enhancement of the electronic density of states close to the Fermi level. Localized disorder leads to a universal, disorder independent, electrical conductivity at low temperatures, of the order of the quantum of conductance. The static conductivity increases with temperature and shows oscillations in the presence of a magnetic field. The graphene magnetic susceptibility is temperature dependent (unlike an ordinary metal) and also increases with the amount of defects. Optical transport properties are also calculated in detail. On the other hand, extended defects induce localized states near the Fermi level. In the absence of electron-hole symmetry, these states lead to a transfer of charge between the defects and the bulk, the phenomenon we call self-doping. The role of electron-electron interactions in controlling self-doping is also analyzed. We also discuss the integer and fractional quantum Hall effect in graphene, the role played by the edge states induced by a magnetic field, and their relation to the almost field independent surface states induced at boundaries. The possibility of magnetism in graphene, in the presence of short-range electron-electron interactions and disorder is also analyzed.

1,237 citations

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TL;DR: In this article, a numerical analysis of surface plasmon waveguides exhibiting both long-range propagation and spatial confinement of light with lateral dimensions of less than 10% of the free-space wavelength is presented.

Abstract: We present a numerical analysis of surface plasmon waveguides exhibiting both long-range propagation and spatial confinement of light with lateral dimensions of less than 10% of the free-space wavelength. Attention is given to characterizing the dispersion relations, wavelength-dependent propagation, and energy density decay in two-dimensional Ag/SiO2/Ag structures with waveguide thicknesses ranging from 12 nm to 250 nm. As in conventional planar insulator-metal-insulator (IMI) surface plasmon waveguides, analytic dispersion results indicate a splitting of plasmon modes—corresponding to symmetric and antisymmetric electric field distributions—as SiO2 core thickness is decreased below 100 nm. However, unlike IMI structures, surface plasmon momentum of the symmetric mode does not always exceed photon momentum, with thicker films (d~50 nm) achieving effective indices as low as n=0.15. In addition, antisymmetric mode dispersion exhibits a cutoff for films thinner than d=20 nm, terminating at least 0.25 eV below resonance. From visible to near infrared wavelengths, plasmon propagation exceeds tens of microns with fields confined to within 20 nm of the structure. As the SiO2 core thickness is increased, propagation distances also increase with localization remaining constant. Conventional waveguiding modes of the structure are not observed until the core thickness approaches 100 nm. At such thicknesses, both transverse magnetic and transverse electric modes can be observed. Interestingly, for nonpropagating modes (i.e., modes where propagation does not exceed the micron scale), considerable field enhancement in the waveguide core is observed, rivaling the intensities reported in resonantly excited metallic nanoparticle waveguides.

1,107 citations

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TL;DR: In this paper, a tight-binding model is used to calculate the band structure of bilayer graphene in the presence of a potential difference between the layers that opens a gap between the conduction and valence bands.

Abstract: A tight-binding model is used to calculate the band structure of bilayer graphene in the presence of a potential difference between the layers that opens a gap $\ensuremath{\Delta}$ between the conduction and valence bands. In particular, a self-consistent Hartree approximation is used to describe imperfect screening of an external gate, employed primarily to control the density $n$ of electrons on the bilayer, resulting in a potential difference between the layers and a density dependent gap $\ensuremath{\Delta}(n)$. We discuss the influence of a finite asymmetry gap $\ensuremath{\Delta}(0)$ at zero excess density, caused by the screening of an additional transverse electric field, on observations of the quantum Hall effect.

1,104 citations

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TL;DR: In this article, the Dzyaloshinskii-Moriya interaction (DMI) provides the microscopic mechanism for the coexistence and strong coupling between ferroelectricity and incommensurate magnetism.

Abstract: With the perovskite multiferroic $R\mathrm{Mn}{\mathrm{O}}_{3}$ $(R=\mathrm{Gd},\mathrm{Tb},\mathrm{Dy})$ as guidance, we argue that the Dzyaloshinskii-Moriya interaction (DMI) provides the microscopic mechanism for the coexistence and strong coupling between ferroelectricity and incommensurate magnetism. We use Monte Carlo simulations and zero-temperature exact calculations to study a model incorporating the double-exchange, superexchange, Jahn-Teller, and DMI terms. The phase diagram contains a multiferroic phase between $A$ and $E$ antiferromagnetic phases, in excellent agreement with experiments.

1,042 citations

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TL;DR: In this article, the intrinsic and Rashba spin-orbit interaction induced gaps in the Dirac-like low-energy band structure of an isolated graphene sheet were derived using second-order perturbation theory.

Abstract: Starting from a microscopic tight-binding model and using second-order perturbation theory, we derive explicit expressions for the intrinsic and Rashba spin-orbit interaction induced gaps in the Dirac-like low-energy band structure of an isolated graphene sheet. The Rashba interaction parameter is first order in the atomic carbon spin-orbit coupling strength $\ensuremath{\xi}$ and first order in the external electric field $E$ perpendicular to the graphene plane, whereas the intrinsic spin-orbit interaction which survives at $E=0$ is second order in $\ensuremath{\xi}$. The spin-orbit terms in the low-energy effective Hamiltonian have the form proposed recently by Kane and Mele. Ab initio electronic structure calculations were performed as a partial check on the validity of the tight-binding model.

898 citations

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TL;DR: In this paper, the authors investigated how the electronic structure evolves from a single graphene layer into bulk graphite by computing the band structure of one, two, and three layers of graphene.

Abstract: Within a tight-binding approach we investigate how the electronic structure evolves from a single graphene layer into bulk graphite by computing the band structure of one, two, and three layers of graphene. It is well known that a single graphene layer is a zero-gap semiconductor with a linear Dirac-like spectrum around the Fermi energy, while graphite shows a semimetallic behavior with a band overlap of about $41\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. In contrast to a single graphene layer, we show that two graphene layers have a parabolic spectrum around the Fermi energy and are a semimetal like graphite; however, the band overlap of $0.16\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ is extremely small. Three and more graphene layers show a clear semimetallic behavior. For 11 and more layers the difference in band overlap with graphite is smaller than 10%.

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TL;DR: In this article, the authors showed that submicrometer sized gold crystals can be 50 times stronger than their bulk counterparts due to the elimination of defects from the crystal in the course of deformation.

Abstract: It has been known for more than half a century that crystals can be made stronger by introducing defects into them, i.e., by strain-hardening. As the number of defects increases, their movement and multiplication is impeded, thus strengthening the material. In the present work we show hardening by dislocation starvation, a fundamentally different strengthening mechanism based on the elimination of defects from the crystal. We demonstrate that submicrometer sized gold crystals can be 50 times stronger than their bulk counterparts due to the elimination of defects from the crystal in the course of deformation.

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TL;DR: In this article, a spin-orbit interaction model for flat graphene is derived from a tight-binding model, which includes the σ and σ-sigma bands, where σ is the intra-atomic spinorbit coupling constant for carbon.

Abstract: A continuum model for the effective spin-orbit interaction in graphene is derived from a tight-binding model which includes the $\ensuremath{\pi}$ and $\ensuremath{\sigma}$ bands. We analyze the combined effects of the intra-atomic spin-orbit coupling, curvature, and applied electric field, using perturbation theory. We recover the effective spin-orbit Hamiltonian derived recently from group theoretical arguments by Kane and Mele. We find, for flat graphene, that the intrinsic spin-orbit coupling ${\ensuremath{\Delta}}_{\mathrm{int}}\ensuremath{\propto}{\ensuremath{\Delta}}^{2}$ and the Rashba coupling due to a perpendicular electric field $\mathcal{E}$, ${\ensuremath{\Delta}}_{\mathcal{E}}\ensuremath{\propto}\ensuremath{\Delta}$, where $\ensuremath{\Delta}$ is the intra-atomic spin-orbit coupling constant for carbon. Moreover we show that local curvature of the graphene sheet induces an extra spin-orbit coupling term ${\ensuremath{\Delta}}_{\mathrm{curv}}\ensuremath{\propto}\ensuremath{\Delta}$. For the values of $\mathcal{E}$ and curvature profile reported in actual samples of graphene, we find that ${\ensuremath{\Delta}}_{\mathrm{int}}l{\ensuremath{\Delta}}_{\mathcal{E}}\ensuremath{\lesssim}{\ensuremath{\Delta}}_{\mathrm{curv}}$. The effect of spin-orbit coupling on derived materials of graphenelike fullerenes, nanotubes, and nanotube caps, is also studied. For fullerenes, only ${\ensuremath{\Delta}}_{\mathrm{int}}$ is important. Both for nanotubes and nanotube caps ${\ensuremath{\Delta}}_{\mathrm{curv}}$ is in the order of a few Kelvins. We reproduce the known appearance of a gap and spin-splitting in the energy spectrum of nanotubes due to the spin-orbit coupling. For nanotube caps, spin-orbit coupling causes spin-splitting of the localized states at the cap, which could allow spin-dependent field-effect emission.

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TL;DR: In this article, the magnetic moment was observed in undoped semiconducting or insulating oxides to become ferromagnetic at room temperature on MgO substrates, where the magnetic field was applied parallel to the film plane.

Abstract: Remarkable room-temperature ferromagnetism was observed in undoped $\mathrm{Ti}{\mathrm{O}}_{2}$, $\mathrm{Hf}{\mathrm{O}}_{2}$, and ${\mathrm{In}}_{2}{\mathrm{O}}_{3}$ thin films. The magnetic moment is rather modest in the case of ${\mathrm{In}}_{2}{\mathrm{O}}_{3}$ films on MgO substrates (while on ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ substrates, it is negative showing diamagnetism) when the magnetic field was applied parallel to the film plane. In contrast, it is very large in the other two cases (about 20 and $30\phantom{\rule{0.3em}{0ex}}\mathrm{emu}∕{\mathrm{cm}}^{3}$ for $200\text{\ensuremath{-}}\mathrm{nm}$-thick $\mathrm{Ti}{\mathrm{O}}_{2}$ and $\mathrm{Hf}{\mathrm{O}}_{2}$ films, respectively). Since bulk $\mathrm{Ti}{\mathrm{O}}_{2}$, $\mathrm{Hf}{\mathrm{O}}_{2}$, and ${\mathrm{In}}_{2}{\mathrm{O}}_{3}$ are clearly diamagnetic, and moreover, there are no contaminations in any substrate, we must assume that the thin film form, which might create necessary defects or oxygen vacancies, would be the reason for undoped semiconducting or insulating oxides to become ferromagnetic at room temperature.

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TL;DR: In this paper, a class of one-dimensional insulating Hamiltonians that, when adiabatically varied in an appropriate closed cycle, define a topological invariant was introduced.

Abstract: We introduce and analyze a class of one-dimensional insulating Hamiltonians that, when adiabatically varied in an appropriate closed cycle, define a ``${Z}_{2}$ pump.'' For an isolated system, a single closed cycle of the pump changes the expectation value of the spin at each end even when spin-orbit interactions violate the conservation of spin. A second cycle, however, returns the system to its original state. When coupled to leads, we show that the ${Z}_{2}$ pump functions as a spin pump in a sense that we define, and transmits a finite, though nonquantized, spin in each cycle. We show that the ${Z}_{2}$ pump is characterized by a ${Z}_{2}$ topological invariant that is analogous to the Chern invariant that characterizes a topological charge pump. The ${Z}_{2}$ pump is closely related to the quantum spin Hall effect, which is characterized by a related ${Z}_{2}$ invariant. This work presents an alternative formulation that clarifies both the physical and mathematical meaning of that invariant. A crucial role is played by time reversal symmetry, and we introduce the concept of the time reversal polarization, which characterizes time reversal invariant Hamiltonians and signals the presence or absence of Kramers degenerate end states. For noninteracting electrons, we derive a formula for the time reversal polarization that is analogous to Berry's phase formulation of the charge polarization. For interacting electrons, we show that Abelian bosonization provides a simple formulation of the time reversal polarization. We discuss implications for the quantum spin Hall effect, and argue in particular that the ${Z}_{2}$ classification of the quantum spin Hall effect is valid in the presence of electron electron interactions.

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TL;DR: In this paper, a fully frequency-dependent algorithm for the calculation of polarizability matrices and quasiparticle energies is presented. Butler et al. used the spectral representation of the involved matrices, and their Hilbert or Kramers-Kronig transforms were used to obtain the polarizable and self-energy matrices at each frequency.

Abstract: Algorithmic details and results of fully frequency-dependent ${G}_{0}{W}_{0}$ calculations are presented. The implementation relies on the spectral representation of the involved matrices and their Hilbert or Kramers-Kronig transforms to obtain the polarizability and self-energy matrices at each frequency. Using this approach, the computational time for the calculation of polarizability matrices and quasiparticle energies is twice as that for a single frequency, plus Hilbert transforms. In addition, the implementation relies on the PAW method, which allows to treat $d$-states with relatively modest effort and permits the reevaluation of the core-valence interaction on the level of the Hartree-Fock approximation. Tests performed on an $sp$ material (Si) and materials with $d$ electrons (GaAs and CdS) yield quasiparticle energies that are very close to previous all-electron pseudopotential and all-electron full-potential linear muffin-tin-orbital calculations.

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TL;DR: In this article, the influence of a simple semi-empirical van der Waals (vdW) correction on the description of dispersive, covalent, and ionic bonds within density functional theory is studied.

Abstract: The influence of a simple semiempirical van der Waals (vdW) correction on the description of dispersive, covalent, and ionic bonds within density functional theory is studied. The correction is based on the asymptotic London form of dispersive forces and a damping function for each pair of atoms. It thus depends solely on the properties of the two atoms irrespective of their environment and is numerically very efficient. The correction is tested in comparison with results obtained using the generalized gradient approximation or the local density approximation for exchange and correlation. The results are also compared with reference values from experiment or quantum chemistry methods. In order to probe the universality and transferability of the semiempirical vdW correction, a range of solids and molecular systems with covalent, heteropolar, and vdW bonds are studied.

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TL;DR: In this paper, the authors exploit the dispersion characteristics of an anisotropic metamaterial crystal that is obliquely cut at its output plane, or has a curved output surface, in order to map the input field distribution onto the crystal's output surface with a compressed angular spectrum, resulting in a ''magnified'' image.

Abstract: Here we suggest and explore theoretically an idea for a far-field scanless optical microscopy with a subdiffraction resolution. We exploit the special dispersion characteristics of an anisotropic metamaterial crystal that is obliquely cut at its output plane, or has a curved output surface, in order to map the input field distribution onto the crystal's output surface with a compressed angular spectrum, resulting in a ``magnified'' image. This can provide a far-field imaging system with a resolution beyond the diffraction limits while no scanning is needed.

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TL;DR: In this paper, a wide class of nanoribbons is characterized by a set of two integers, p, q, and then the width is defined in terms of $p$ and $q$ electronic properties.

Abstract: Nanoribbons (nanographite ribbons) are carbon systems analogous to carbon nanotubes We characterize a wide class of nanoribbons by a set of two integers $⟨p,q⟩$, and then define the width $w$ in terms of $p$ and $q$ Electronic properties are explored for this class of nanoribbons Zigzag (armchair) nanoribbons have similar electronic properties to armchair (zigzag) nanotubes The band gap structure of nanoribbons exhibits a valley structure with streamlike sequences of metallic or almost metallic nanoribbons These sequences correspond to equiwidth curves indexed by $w$ We reveal a peculiar dependence of the electronic property of nanoribbons on the width $w$

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TL;DR: In this article, an electrostatically created n-p junction separating the electron and hole gas regions in a graphene monolayer was shown to transmit only those quasiparticles that approach it almost perpendicularly to the np interface.

Abstract: We show that an electrostatically created n-p junction separating the electron and hole gas regions in a graphene monolayer transmits only those quasiparticles that approach it almost perpendicularly to the n-p interface. Such a selective transmission of carriers by a single n-p junction would manifest itself in nonlocal magnetoresistance effect in arrays of such junctions and determines the unusual Fano factor in the current noise universal for the n-p junctions in graphene.

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TL;DR: In this article, the application of variational density functional perturbation theory (DFPT) to lattice dynamics and dielectric properties is discussed within the plane-wave pseudopotential formalism.

Abstract: The application of variational density functional perturbation theory (DFPT) to lattice dynamics and dielectric properties is discussed within the plane-wave pseudopotential formalism. We derive a method to calculate the linear response of the exchange-correlation potential in the GGA at arbitrary wavevector. We introduce an efficient self-consistent solver based on all-bands conjugate-gradient minimization of the second order energy, and compare the performance of preconditioning schemes. Lattice-dynamical and electronic structure consequences of space-group symmetry are described, particularly their use in reducing the computational effort required. We discuss the implementation in the CASTEP DFT modeling code, and how DFPT calculations may be efficiently performed on parallel computers. We present results on the lattice dynamics and dielectric properties of $\ensuremath{\alpha}$-quartz, the hydrogen bonded crystal $\mathrm{Na}\mathrm{H}{\mathrm{F}}_{2}$ and the liquid-crystal-forming molecule 5CB. Excellent agreement is found between theory and experiment within the GGA.

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TL;DR: In this article, it was shown that there exists a radius-dependent critical layer thickness below which no interfacial dislocation should be introduced, and that this critical thickness becomes infinite for radii less than some critical value, below which arbitrarily thick coherent layers should be obtainable.

Abstract: We consider strained layers at the top of free-standing nanowires. We show that there exists a radius-dependent critical layer thickness below which no interfacial dislocation should be introduced. This critical thickness becomes infinite for radii less than some critical value, below which arbitrarily thick coherent layers should be obtainable. Implicit equations allowing the calculation of these critical dimensions from material parameters are given. These are derived from an evaluation of the elastic energy stored in the system with a coherent interface, the areal density of which is shown to be much less than in a laterally infinite system.

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TL;DR: In this article, the authors quantify how well matrix product states approximate exact ground states of one-dimensional quantum spin systems as a function of the number of spins and the entropy of blocks of spins.

Abstract: We quantify how well matrix product states approximate exact ground states of one-dimensional quantum spin systems as a function of the number of spins and the entropy of blocks of spins. We also investigate the convex set of local reduced density operators of translational invariant systems. The results give a theoretical justification for the high accuracy of renormalization group algorithms and justifies their use even in the case of critical systems.

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TL;DR: In this article, an analytic approach was proposed to determine the tension and bending rigidities of CNTs directly from the interatomic potential, which is useful in the study of multi-wall carbon nanotubes.

Abstract: Young's modulus and the thickness of single wall carbon nanotubes (CNTs) obtained from prior atomistic studies are largely scattered. In this paper we establish an analytic approach to bypass atomistic simulations and determine the tension and bending rigidities of graphene and CNTs directly from the interatomic potential. The thickness and elastic properties of graphene and CNTs can also be obtained from the interatomic potential. But the thickness, and therefore elastic moduli, also depend on type of loading (e.g., uniaxial tension, uniaxial stretching, equibiaxial stretching), as well as the nanotube radius $R$ and chirality when $Rl1\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. This explains why the thickness obtained from prior atomistic simulations is scattered. This analytic approach is particularly useful in the study of multiwall CNTs since their stress state may be complex even under simple loading (e.g., uniaxial tension) due to the van der Waals interactions between nanotube walls. The present analysis also provides an explanation of Yakobson's paradox that the very high Young's modulus reported from the atomistic simulations together with the shell model may be due to the not-well-defined CNT thickness.

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TL;DR: In this article, a model of the electronic structure and the associated dynamics of the nitrogen-vacancy center in diamond was presented for the occurrence of optically induced spin polarization, for the change of emission level with spin polarization and for new experimental measurements of transient emission.

Abstract: Symmetry considerations are used in presenting a model of the electronic structure and the associated dynamics of the nitrogen-vacancy center in diamond. The model accounts for the occurrence of optically induced spin polarization, for the change of emission level with spin polarization and for new experimental measurements of transient emission. The rate constants given are in variance to those reported previously.

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TL;DR: In this paper, a detailed investigation of thermoelectric compounds and their quasibinary alloys is presented, and it is shown that the combination of transport properties and band structure features has the most promising performance for thermolectric applications.

Abstract: Results of detailed investigations of ${\mathrm{Mg}}_{2}{B}^{\mathrm{IV}}$ $({B}^{\mathrm{IV}}=\mathrm{Si},\phantom{\rule{0.3em}{0ex}}\mathrm{Ge},\phantom{\rule{0.3em}{0ex}}\mathrm{Sn})$ compounds and their quasibinary alloys are presented. Our analysis revealed that ${\mathrm{Mg}}_{2}\mathrm{Si}\text{\ensuremath{-}}{\mathrm{Mg}}_{2}\mathrm{Sn}$ system has the most promising for thermoelectric applications combination of transport properties and band structure features. The $n$-type ${\mathrm{Mg}}_{2}{\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Sn}}_{x}$ solid solutions were studied in broad range of compositions and electron concentration (up to $5\ifmmode\times\else\texttimes\fi{}{10}^{20}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$). Temperature dependencies of figure of merit were determined in temperature range $300\text{--}870\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ using results of simultaneous measurements of Seebeck coefficient, electrical, and thermal conductivities. The alloy of optimized composition has reproducible figure of merit $Z{T}_{\mathrm{max}}=1.1$. The results of the present study are compared with the data for best modern thermoelectrics.

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TL;DR: In this paper, the structural, electronic, magnetic, and ferroelectric properties of a cubic perovskite-type reference lattice were predicted using accurate density functional calculations and the equilibrium structural parameters were found to be in very good agreement with the experimental findings.

Abstract: The magnetoelectric behavior of $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_{3}$ has been explored on the basis of accurate density functional calculations. We are able to predict structural, electronic, magnetic, and ferroelectric properties of $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_{3}$ correctly without including any strong correlation effect in the calculation. Unlike earlier calculations, the equilibrium structural parameters are found to be in very good agreement with the experimental findings. In particular, the present calculation correctly reproduced experimentally observed elongation of cubic perovskitelike lattice along the [111] direction. At high pressure we predicted a pressure-induced structural transition from rhombohedral $(R3c)$ to an orthorhombic $(Pnma)$ structure. The total-energy calculations at expanded lattice show two lower energy ferroelectric phases (with monoclinic $Cm$ and tetragonal $P4mm$ structures), closer in energy to the ground-state phase. Spin-polarized band-structure calculations show that $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_{3}$ will be an insulator in $A$- and $G$-type antiferromagnetic phases and a metal in $C$-type antiferromagnetic, ferromagnetic configurations, and in the nonmagnetic state. Chemical bonding in $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_{3}$ has been analyzed using partial density of states, charge density, charge transfer, electron localization function, Born-effective-charge tensor, and crystal orbital Hamiltonian population analyses. Our electron localization function analysis shows that stereochemically active lone-pair electrons are present at the Bi sites which are responsible for displacements of the Bi atoms from the centrosymmetric to the noncentrosymmetric structure and hence the ferroelectricity. A large ferroelectric polarization of $88.7\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{C}∕{\mathrm{cm}}^{2}$ is predicted in accordance with recent experimental findings, but differing by an order of magnitude from earlier experimental values. The strong spontaneous polarization is related to the large values of the Born-effective charges at the Bi sites along with their large displacement along the [111] direction of the cubic perovskite-type reference structure. Our polarization analysis shows that partial contributions to polarization from the Fe and O atoms almost cancel each other and the net polarization present in $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_{3}$ mainly $(g98%)$ originates from Bi atoms. We found that the large scatter in experimentally reported polarization values in $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_{3}$ is associated with the large anisotropy in the spontaneous polarization.

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TL;DR: In this paper, the intrinsic spin Hall effect is exactly quantized in integer units of a topological charge, where the number of extended edge states crossing the Fermi level is dictated by (exactly equal to) the bulk topology charge.

Abstract: We propose models of two-dimensional paramagnetic semiconductors where the intrinsic spin Hall effect is exactly quantized in integer units of a topological charge. The model describes a topological insulator in the bulk and a ``holographic metal'' at the edge, where the number of extended edge states crossing the Fermi level is dictated by (exactly equal to) the bulk topological charge. We also demonstrate the spin Hall effect explicitly in terms of the spin accumulation caused by the adiabatic flux insertion.

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TL;DR: The SMEAGOL algorithm as discussed by the authors constructs surface Green's functions describing the currentvoltage probes, which can be used to evaluate the I-V characteristics of atomic junctions, which integrates the nonequilibrium Green's function method with density functional theory.

Abstract: Ab initio computational methods for electronic transport in nanoscaled systems are an invaluable tool for the design of quantum devices. We have developed a flexible and efficient algorithm for evaluating I-V characteristics of atomic junctions, which integrates the nonequilibrium Green’s function method with density functional theory. This is currently implemented in the package SMEAGOL. The heart of SMEAGOL is our scheme for constructing the surface Green’s functions describing the current-voltage probes. It consists of a direct summation of both open and closed scattering channels together with a regularization procedure of the Hamiltonian and provides great improvements over standard recursive methods. In particular it allows us to tackle material systems with complicated electronic structures, such as magnetic transition metals. Here we present a detailed description of SMEAGOL together with an extensive range of applications relevant for the two burgeoning fields of spin and molecular electronics.

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TL;DR: In this paper, the magnetic and structural transformations in the Heusler-based system were studied in the composition range $0.05, 0.16, and 0.25, respectively, and the magnetic coupling in both austenitic and martensitic states is ferromagnetic.

Abstract: The magnetic and structural transformations in the Heusler-based system ${\mathrm{Ni}}_{0.50}{\mathrm{Mn}}_{0.50\ensuremath{-}x}{\mathrm{In}}_{x}$ are studied in the composition range $0.05\ensuremath{\leqslant}x\ensuremath{\leqslant}0.25$. While the cubic phase is preserved in the range $0.165\ensuremath{\leqslant}x\ensuremath{\leqslant}0.25$, we find the presence of martensitic transformations in alloys with $x\ensuremath{\leqslant}0.16$. In a critical composition range $0.15\ensuremath{\leqslant}x\ensuremath{\leqslant}0.16$, the magnetic coupling in both austenitic and martensitic states is ferromagnetic. Magnetic field-induced structural transitions are also found in the $x=0.16$ alloy, whereby the structural transition temperature shifts by $42\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ in a field of $50\phantom{\rule{0.3em}{0ex}}\mathrm{kOe}$.